A BP–MF–EP Based Iterative Receiver for Joint Phase Noise Estimation, Equalization, and Decoding

In this letter, with combined belief propagation (BP), mean field (MF), and expectation propagation (EP), an iterative receiver is designed for joint phase noise estimation, equalization, and decoding in a coded communication system. The presence of the phase noise results in a nonlinear observation model. Conventionally, the nonlinear model is directly linearized by using the first-order Taylor approximation, e.g., in the state-of-the-art soft-input extended Kalman smoothing approach (Soft-in EKS). In this letter, MF is used to handle the factor due to the nonlinear model, and a second-order Taylor approximation is used to achieve Gaussian approximation to the MF messages, which is crucial to the low-complexity implementation of the receiver with BP and EP. It turns out that our approximation is more effective than the direct linearization in the Soft-in EKS, leading to a significant performance improvement with similar complexity as demonstrated by simulation results.